有限阿贝尔群中砖块的周期性

本文介绍了有限阿贝尔群的周期性砖瓦(PT)属性。若有限阿贝尔群中每个非周期性集合通过平移搭配都存在周期性砖瓦补集，则称该群具有PT属性。该概念超越了具有哈伊jos属性的群的范围。我们给出了完全分类的循环群中拥有PT属性的情形，并识别了某些非循环群同时拥有PT属性但不满足哈伊jos属性。作为副产品，我们获得了新的一族满足“砖瓦⟹谱谱”蕴含关系的群。 Furthermore, for elementary $p$-groups with the PT property, by analyzing the structure of tiles, we prove that every tile is a complete set of representatives of the cosets of some subgroup. Furthermore, for elementary $p$-groups with the PT property, by analyzing the structure of tiles, we prove that every tile is a complete set of representatives of the cosets of some subgroup.